The expected time for fixation given its occurrence, and the probability of fixa-
tion of a new mutant allele in populations subject to various biological phe-
nomena are analyzed using the approach of the ancestral process. First, the
paper of Tajima (1990) is analyzed, and the missing or incomplete proofs are
fully worked out in this Master thesis in order to familiarize ourselves with
calculations of fixation times. Our study of Tajima’s paper helps to show the
importance of the fixation time in some biological phenomena. Thereafter, we
extend the work of Tajima (1990) by introducing the effect of natural selec-
tion in the model. Using a diffusion approximation, the work of Mano (2009)
provides an interesting result about the expected time of fixation given its oc-
currence. We derived an alternative method that uses an ancestral process that
approximates well Mani’s result. Simulations are made to verify the accuracy
ofthenewapproach.Finally,onemodelsubjecttogeneconversionisanalyzed,
since this phenomenon, in the presence of bias, has a similar effect as selection.
We deduce an analytical result for the probability of fixation of a new mutant
in the population. Finally, simulations are made to determine the probability
of fixation and the time of fixation given its occurrence when rates are too large
to be calculated analytically.